Having been a fan of Bleach and Naruto, and am now marathoning One Piece, I think I can comment on this.

In my opinion, all three of these shows got popular for widely different reasons. So to illustrate that, let me review them in the order that I saw them;

Naruto

Yep, Naruto was the first of the HST that I watched. Coming off of the success of Dragon Ball Z, as a tween, I felt that Naruto was the perfect replacement for the time slot on Toonami. The show opens with showing just how much of an outcast Naruto is, and alludes to the immense power he had locked inside of himself, similar to the power that Goku had locked inside of him before he turned into a Super Saiyan. Naruto's biggest strength was in the lead character, and his struggles to make friends with the other superpowered ninja of the land. The show really hooked me when Naruto, Sakura and Sasuke had to actually work together to steal bells from Kakashi. I guess in my 11 year old mind, it was cool to see a hot-headed outcast, a smart but annoying girl, and a emo guy work together to solve an objective. I haven't kept up with Naruto since the original series ended, though, so I couldn't comment on the new additions to the formula (I am looking at you, Juubidara.)

Bleach

The second one of the HST that I watched as a kid, but a few years older into my teens this time. What drew me into this show were the fight scenes in almost every episode, and the spiritual concept of the Soul Reapers and Hollows. Now, I didn't watch Yu Yu Hakusho as a kid, so as far as I knew, this was all a new experience. The large cast of unique characters was also a plus for me, as no matter who you are, you always found a character that you could relate with, since Ichigo is the blandest of all 3 HST protagonists.

One Piece

One Piece is the special one in my anime history, as I watched a little bit of it as a kid, but dropped it for a reason that I don't remember. I am watching it now though, and what initially drew me in was, much like Fairy Tail, was the sense of adventure in the world of One Piece. The heroes are always sailing to new, exciting lands to explore, which is a stark contrast to Naruto staying locked on land, and Bleach jumping between the Soul Society and Ichigo's home town. Luffy has to be one of the dumbest of the HST, and many of his actions right now don't seem to make any sense until one of his friends is hurt. The biggest draw imo is the overall atmosphere of the world, and the back stories of the various villains and heroes that Luffy and his crew of misfits meet along the way.

Conclusion

At least in my experience, Naruto, Bleach and One Piece became successful for different reasons. Naruto roped audiences in with Naruto himself as a hook, and his struggles against a society that rejected him before he was even born. Bleach pulled people in with it's vast selection of unique characters and non-stop sword fighting action sequences. One Piece instilled a sense of adventure from the start, and kept audiences coming back to see what new place Luffy and his crew would come around to next, with only the veil of the One Piece being the overarching motivation behind all nearly 700 episodes. Great work as usual Tom and Matt!

Out of these three shows the only one that had me hooked for a while was
Bleach, honestly this was a show that kind of renewed my interest in anime
After a short hiatus, I'm with Murphy here, that opener was off the hook!, and also
Being only 16 at the time I had a crush on Rukiya,
however my first Shonen anime post DBZ was Ruroni Ken-shin back on toonami, and it's still one
Of my favorites,
I guess for me what makes a Shonen pilot episode click, depends on how radical the lead hero feels from get go, for example take Kenshin a samurai who in the past killed so many people so brutally and efficiently, that he was known and feared as the manslayer, in the present he is reformed and living a pacifist philosophy with acrew of villagers, until baddies show up then he kicks all kinds of ass, all with out killing them, one minute he was a goofy dork with a dumb voice,
Then pow!, he was cool headed steely eyed badass, I was game,
So yeah I think you guys are on the money!,
By the way with all this talk of Shonen lately, how do you guys Feel about romance in anime? Do you think there should be more love story's like that of
Escaflowne, or perhaps more intimacy especially with the way that shonen in particular seems to avoid the subject, I Agree with Tom that it feels a bit suspect,

@Vapovile: to be fair Luffy's made some rather good decisions of late. On Fishman island of course he'd choose to go save his friends before anything else, they were his priority. The fishman were none of his business anyways. Joining with Law was obviously the best part of the New World so far so you can't fault him for that, and when he knocked out Ceasar he didn't even do it for someone in his crew, he did it because he was a total douche. And finally, him deciding to fight in the stadium for Ace's fruit was a good thing. It may have redirected from the plan, but a lot of things ended up changing in their plans. and it fell apart anyways.

As for Naruto I find that yes, it was a much better series before the time skip. Naruto wasn't so weird for Sausuke yet. The side characters actually had a purpose and weren't overshadowed by the main character all the time, which is completely true now. I also felt Naruto was getting too cocky through the series and thankfully Itachi gave him a sort of reality check. All in all it's picked up a little more lately because you know its the end and Kubo is moving it along a little faster.

Bleach has been a roller coaster of sorts for many. The Winter War dragged on and in the end disappointed a lot of people. The series itself did good in soul society, but went down during his training arc, but then back up in hueco mundo. Then back down during the winter war. Recently it's going back up thanks to the final arc battles, but it's still making a complete turn for better, and more needs to be seen.

Now for my favorite, One Piece. Now I'm not going to say it is perfect like a stupid fan boy. But so far this time skip has been a great time to see. Fishman island really did drag on and it kind of got in the way of the New World, even though it was really just meant to show off the maturity of the Strawhats over the years. Now for me, One Piece's strongest point I think is not only does Luffy make for a great main character (even if he is stupid but come on, giving him the full package wouldn't be fair :P), but also the fact that his crew is just all sorts of interesting. And all in all, they all have usefulness. Zoro and Sanji back him up and take out the strongest second in commands. Nami is the navigator and pretty much the brains of the Strawhats aside from Robin. All of them have jobs they do because they trust in each other to do it, something that neither Naruto or Bleach had for a while. Both Naruto and Ichigo felt they had to shoulder everything and beat everyone, but Luffy has always known that he would have died by now without his crew and believes in their strength as much as his own. That is part of why I think he's still a great main character. There are many other things about One Piece I could talk about like what you said with the amazing adventure and the endless possibilities with the different islands, but I think I've said enough on the subject XD

@Jinbeifan1: Well I am speaking about the Luffy I have seen so far, since I am only a few episodes before the Aarlong Park arc, as I am only recently starting this show again. I am not going to read your first paragraph for fear of spoilers XD.

I love tom how given your fits with kill la kill the good part of shonen is that it gets right to the point and doesn't spend time on you know world building (I mean really the world of bleach is totally add hoc and makes no sense) getting you to care about characters (though one piece may)...but really bleach is all action and naruto is mostly about switching between action and stupid humor...but then I suppose I may be to serious for shonen I suppose....